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Lattice-Renormalization of the Polyakov Loop
Full text linkZantow F. Lattice-Renormalization of the Polyakov Loop. Bielefeld: Fakultät für Physik; 2003
Effective Polyakov-loop theory for pure Yang-Mills from strong coupling expansion
Full text linkLattice Yang-Mills theories at finite temperature can be mapped onto effective 3d spin systems, thus facilitating their numerical investigation. Using strong-coupling expansions we derive effective actions for Polyakov loops in the SU(2) and SU(3) cases and investigate the effect of higher order corrections. Once a formulation is obtained which allows for Monte Carlo analysis, the nature of the phase transition in both classes of models is investigated numerically, and the results are then used to predict – with an accuracy within a few percent – the deconfinement point in the original 4d Yang-Mills pure gauge theories, for a series of values of Nt at once
GHOST COHOMOLOGIES AND HIDDEN SPACE–TIME SYMMETRIES
No full textWe observe and study new nonlinear global space-time symmetries of the full ghost + matter action of RNS superstring theory. We show that these surprising new symmetries are generated by the special worldsheet currents (physical vertex operators) of RNS superstring theory, violating the equivalence of superconformal ghost pictures. We review the questions of BRST-invariance and nontriviality of picture-dependent vertex operators and show their relation to hidden space-time symmetries and hidden space-time dimensions. In particular, we relate the space-time transformations, induced by picture-dependent currents, to the symmetries observed in the 2T physics approach. © World Scientific Publishing Company.Bars I, 1999, PHYS REV D, V59, DOI 10.1103-PhysRevD.59.045019; Bars I, 1999, PHYS REV D, V59, DOI 10.1103-PhysRevD.59.125004; Bars I, 1999, PHYS LETT B, V457, P275, DOI 10.1016-S0370-2693(99)00582-1; KLEBANOV IR, 1991, MOD PHYS LETT A, V6, P3273, DOI 10.1142-S021773239100378X; KLEBANOV IR, 1993, PHYS REV LETT, V71, P3243, DOI 10.1103-PhysRevLett.71.3243; Kogan II, 2003, INT J MOD PHYS A, V18, P1827, DOI 10.1142-S0217751X03013715; LIAN BH, 1991, PHYS LETT B, V254, P417, DOI 10.1016-0370-2693(91)91177-W; Polyakov D, 2005, INT J MOD PHYS A, V20, P2603, DOI 10.1142-S0217751X05020999; Polyakov D, 2002, PHYS REV D, V65, DOI 10.1103-PhysRevD.65.084041; POLYAKOV D, IN PRESS INT J MOD P; Polyakov D, 2005, INT J MOD PHYS A, V20, P4001, DOI 10.1142-S0217751X05024274; VERLINDE E, 1987, PHYS LETT B, V192, P95, DOI 10.1016-0370-2693(87)91148-8; WITTEN E, 1992, NUCL PHYS B, V373, P187, DOI 10.1016-0550-3213(92)90454-J57
Improved hadronic measurements and spectral sums on the lattice
No full textIn this thesis we address several topics of lattice QCD.
As a first project we perform calculations of ground and excited states of light mesons. Especially the extraction of the excited states turns out be very difficult. Therefore we utilize the variational method, which requires the construction of a rich basis of different interpolating fields, i.e., lattice discretized operators which have the same quantum number as the desired states. To build such a basis we consider quarks with different spatial wavefunctions, including some that mimic orbital excitations.
In the second project, we develop a new improvement scheme to compute estimates of all-to-all quark propagators, i.e., quark propagators which connect each point on the lattice to all others. For that purpose we decompose the lattice in two disjoint regions or domains which allows to significantly reduce the amount of random variables used in the estimation process. As a first major application of this improvement scheme, we compute the spectrum of heavy-light hadrons, i.e., hadrons containing one very heavy quark (bottom) and one or more light quarks (up, down, strange). To reduce the computational costs for the heavy quark, we describe it by means of the lowest order of heavy quark effective theory and thus treat it as infinitely heavy. From our calculations we are able to extract several ground and excited meson states and even a number of baryon ground states.
In the last project, we study two very important features of QCD: Confinement and spontaneous breaking of chiral symmetry. Both of them are temperature dependent: As the temperature is increased above a critical value, the theory becomes deconfined and chiral symmetry is restored. The temperature, at which these phase transitions take place, is approximately the same at least for zero baryon density. To study a possible connection between these phenomena, we try to relate the order parameters of the phase transitions.
In pure Yang-Mills theory the order parameter for the confinement-deconfinement transition is the Polyakov loop. The order parameter for the spontaneous breaking of chiral symmetry is given by the chiral condensate, which is related to the eigenvalues of the Dirac operator. It has been shown that also the Polyakov loop can be expressed in terms of these eigenvalues, as a spectral sum. In a first step we perform a numerical study of these sums. We find that the ordinary Polyakov loop is governed by the ultraviolet modes of the Dirac operator. Therefore, in a second step we define a new order parameter for confinement, the "dressed Polyakov loop". This quantity has two advantages: It can be expressed as a spectral sum which has a better convergence behavior (infrared dominated) and it is closely related to the quark condensate via a Fourier transformation. Also the spectral sums for the dressed Polyakov loop are investigated numerically
Fluid dynamics of NSR strings
No full textWe show that the renormalization group flows of the massless superstring modes in the presence of fluctuating D-branes satisfy the equations of fluid dynamics. In particular, we show that the D-brane's U(1) field is related to the velocity function in the Navier-Stokes equation while the dilaton plays the role of the passive scalar advected by the turbulent liquid. This leads us to suggest a possible isomorphism between the off-shell superstring theory in the presence of fluctuating D-branes and the fluid mechanical degrees of freedom. © World Scientific Publishing Company.D'Hoker E, 2002, NUCL PHYS B, V636, P3, DOI 10.1016-S0550-3213(02)00431-5; FEIGENBAUM MJ, 1978, J STAT PHYS, V19, P25, DOI 10.1007-BF01020332; FRADKIN ES, 1985, NUCL PHYS B, V261, P1, DOI 10.1016-0550-3213(85)90559-0; FRIEDAN D, 1986, NUCL PHYS B, V271, P93; GAWEDZKI K, 1995, PHYS REV LETT, V75, P3834; Gubser SS, 1998, PHYS LETT B, V428, P105, DOI 10.1016-S0370-2693(98)00377-3; KNIZHNIK VG, 1989, USP FIZ NAUK+, V159, P401, DOI 10.3367-UFNr.0159.198911a.0401; KOBA Z, 1969, NUCL PHYS B, VB 12, P517, DOI 10.1016-0550-3213(69)90071-6; Kogan I, 2003, PHYS ATOM NUCL+, V66, P2062, DOI 10.1134-1.1625749; Kogan II, 2003, INT J MOD PHYS A, V18, P1827, DOI 10.1142-S0217751X03013715; KRAICHNA.RH, 1968, PHYS FLUIDS, V11, P945, DOI 10.1063-1.1692063; KRAICHNAN RH, 1994, PHYS REV LETT, V72, P1016, DOI 10.1103-PhysRevLett.72.1016; Maldacena J M, 1998, ADV THEOR MATH PHYS, V2, P231, DOI DOI 10.1023-A:1026654312961; Polyakov A, 2000, NUCL PHYS B, V581, P116, DOI 10.1016-S0550-3213(00)00183-8; Polyakov AM, 1997, NUCL PHYS B, V486, P23, DOI 10.1016-S0550-3213(96)00601-3; Polyakov D, 2002, PHYS REV D, V65, DOI 10.1103-PhysRevD.65.084041; POLYAKOV D, HEPTH0401009; VERLINDE E, 1987, PHYS LETT B, V192, P95, DOI 10.1016-0370-2693(87)91148-8; Witten E., 1998, ADV THEOR MATH PHYS, V2, P253, DOI DOI 10.1016-S0370-1573(99)00083-644
GL(1) charged states in twistor string theory
No full textWe discuss the appearance of the GL(1) charged physical operators in the twistor string theory. These operators are shown to be BRST-invariant and non-trivial and some of their correlators and conformal β-functions are computed. Remarkably, the non-conservation of the GL(1) charge in interactions involving these operators, is related to the anomalous term in the Kac-Moody current algebra. While these operators play no role in the maximum helicity violating (MHV) amplitudes, they are shown to contribute non-trivially to the non-MHV correlators in the presence of the worldsheet instantons. We argue that these operators describe the non-perturbative dynamics of solitons in conformal supergravity. The exact form of such solitonic solutions is yet to be determined. © 2005 Published by Elsevier B.V.Azcarraga J., 1989, PHYS REV LETT, V3, P2443; Berkovits N., 2004, JHEP, V0404; Berkovits N., 2004, JHEP, V0408, P009; CACHAZO F, 2004, JHEP, V410; Gubser SS, 1998, PHYS LETT B, V428, P105, DOI 10.1016-S0370-2693(98)00377-3; Maldacena J M, 1998, ADV THEOR MATH PHYS, V2, P231, DOI DOI 10.1023-A:1026654312961; POLYAKOV D, HEPTH0406079; POLYAKOV D, IN PRESS INT J MOD P; Witten E., 1998, ADV THEOR MATH PHYS, V2, P253, DOI DOI 10.1016-S0370-1573(99)00083-6; Witten E., HEPTH9112056; Witten E, 2004, COMMUN MATH PHYS, V252, P189, DOI 10.1007-s00220-004-1187-344
Wilson-Polyakov surfaces and M-theory branes
No full textIn this paper, we study the M-brane description of the Wilson-Polyakov surfaces in six-dimensional (2, 0) field theory at finite temperature. We investigate the membrane solution dual to a straight Wilons-Polyakov surface and compute the interaction potential between two parallel straight strings by using AdS/CFT correspondence. Furthermore we discuss the M5-brane solutions dual to various Wilson-Polyakov surfaces. Finally we obtain a universal result about M5-brane solutions in generic backgrounds.Physics, Particles & FieldsSCI(E)2ARTICLE5nul
New superstring isometries and hidden dimensions
No full textWe study the hierarchy of hidden space-time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space-time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ∼ H -n-2(n andgt; 0) and associate these generators with a chain of hidden space-time dimensions, with each ghost cohomology Hn ∼ H -n-2 contributing an extra dimension. Namely, we show that each ghost cohomology Hn ∼ H-n-2 of noncritical superstring theory in d-dimensions contains d + n + 1 α-symmetry generators and the generators from Hk ∼ H-k-2, 1 andlt; k andlt; n, combined together, extend the space-time isometry group from the naive SO(d, 2) to SO(d + n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space-time dimension. © World Scientific Publishing Company.Bars I, 1999, PHYS REV D, V59, DOI 10.1103-PhysRevD.59.045019; Bars I, 1999, PHYS REV D, V59, DOI 10.1103-PhysRevD.59.125004; Bars I, 1999, PHYS LETT B, V457, P275, DOI 10.1016-S0370-2693(99)00582-1; Bars I, 1997, PHYS REV D, V55, P2373, DOI 10.1103-PhysRevD.55.2373; KLEBANOV IR, 1991, MOD PHYS LETT A, V6, P3273, DOI 10.1142-S021773239100378X; KLEBANOV IR, 1993, PHYS REV LETT, V71, P3243, DOI 10.1103-PhysRevLett.71.3243; LIAN BH, 1991, PHYS LETT B, V254, P417, DOI 10.1016-0370-2693(91)91177-W; Polyakov D, 2007, INT J MOD PHYS A, V22, P1375, DOI 10.1142-S0217751X07035148; Polyakov D, 2007, INT J MOD PHYS A, V22, P2441, DOI 10.1142-S0217751X07036269; Vafa C, 1996, NUCL PHYS B, V469, P403, DOI 10.1016-0550-3213(96)00172-1; WITTEN E, 1992, NUCL PHYS B, V373, P187, DOI 10.1016-0550-3213(92)90454-J44
CONFORMAL MODULI AND b-c PICTURES FOR NSR STRINGS
No full textWe explore the geometry of superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for NSR strings, free of picture-changing complications. The sigma-model generating functional is constructed by the integration over the bosonic and fermionic moduli, corresponding to insertions of the vertex operators in scattering amplitudes. While the integration over the supermoduli leads to the standard picture-changing insertions, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c fermionic ghosts with the ghost number -1. Important example of the b-c ghost pictures involves the vertex operators in integrated and unintegrated forms. We obtain the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR theory contain the global singularities, leading to the phenomenon of ghost-matter mixing and the appearance of nonperturbative D-brane creation operators. © World Scientific Publishing Company.FRADKIN ES, 1985, NUCL PHYS B, V261, P1, DOI 10.1016-0550-3213(85)90559-0; FRIEDAN D, 1986, NUCL PHYS B, V271, P93; Gubser SS, 1998, PHYS LETT B, V428, P105, DOI 10.1016-S0370-2693(98)00377-3; KNIZHNIK VG, 1989, USP FIZ NAUK+, V159, P401, DOI 10.3367-UFNr.0159.198911a.0401; KOBA Z, 1969, NUCL PHYS B, VB 12, P517, DOI 10.1016-0550-3213(69)90071-6; Kogan II, 2003, INT J MOD PHYS A, V18, P1827, DOI 10.1142-S0217751X03013715; Maldacena J M, 1998, ADV THEOR MATH PHYS, V2, P231, DOI DOI 10.1023-A:1026654312961; OHTA N, 1986, PHYS REV D, V33, P1681, DOI 10.1103-PhysRevD.33.1681; OHTA N, 1986, PHYS LETT B, V179, P349; Polchinski J, 1995, PHYS REV LETT, V75, P4724, DOI 10.1103-PhysRevLett.75.4724; Polyakov D, 2002, PHYS REV D, V65, DOI 10.1103-PhysRevD.65.084041; VERLINDE E, 1987, PHYS LETT B, V192, P95, DOI 10.1016-0370-2693(87)91148-8; Witten E., 1998, ADV THEOR MATH PHYS, V2, P253, DOI DOI 10.1016-S0370-1573(99)00083-688
Geração radiativa de repulsão vetorial para quarks leves
Full text linkDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-Graduação em Física, Florianópolis, 2014Abstract: We apply a non-perturbative analytical method, known as the Optimized PerturbationTheory (OPT), to the Polyakov-Nambu-Jona-Lasinio (PNJL) model in order to investigate physical quantities associated with the QCD phase transitions. We consider the Taylor expansion of the pressure in powers of µ/T obtaining the second cumulant (c2) which is associated to the quark number susceptibility. We discuss how the OPT nite Nc radiative (quantum) corrections induce a contribution to the pressure which behaves as a vector repulsion even when such a channel is absent in the original classical potential. Our results are then compared with the ones furnished by lattice QCD simulations and by the large-Nc approximation showing that, physically, the OPT results resemble those furnished by the latter approximation when a repulsive vector channel is explicitly included in the classical potential. In this case, both approximations fail to correctly describe the Stefan-Boltzmann limit at high temperatures. We discuss how this problem can be circumvented by taking the couplings to be temperature dependent so as to simulate the phenomenon of asymptotic freedom. Since this is the first time the OPT is applied to the PNJL we also discuss many technicalities associated with the evaluation of two loop (exchange) diagrams.Neste trabalho o método analítico não perturbativo conhecido como Teoria de Perturbação Otimizada (OPT) é aplicada ao modelo de Polyakov-Nambu-Jona-Lasinio (PNJL) para que quantidades físicas, associadas com as transições de fase da QCD, possam ser calculadas. A expansão da pressão em potências de µ/T é considerada para obter o segundo cumulante (c2) que é uma quantidade relacionada com a susceptibilidade do número de quarks. Primeiramente discutimos como as correções radiativas de Nc finito geradas pela OPT produzem uma contribuição que se comporta como um termo vetorial repulsivo mesmo quando este tipo de canal está ausente no potencial clássico original. Em seguida, nossos resultados são comparados com aqueles fornecidos pelas simulações na rede e também pela aproximação de Nc grande(LN). Fisicamente, os resultados da OPT são similares aqueles fornecidos pela aproximação LN quando um canal vetorial repulsivo é explicitamente incluido no potencial clássico. Neste caso, nenhuma destas aproximações analíticas produz corretamente o limite de Stefan Boltzmann para altas temperaturas. Contudo, nossos resultados sugerem como estes problemas podem ser contornados tomando-se as constantes de acoplamento como sendo dependentes da temperatura, de maneira que o fenômeno da liberdade assimptótica possa ser simulado. Esta é a primeira vez que a OPT é aplicada ao modelo de PNJL e por isto vários aspectos técnicos relacionados com o cálculo de diagramas de dois laços são também aqui apresentados
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